Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
The 21-year-old, who enjoyed a brief spell on loan with Wanderers during the latter stages of the season, will sign a one-year deal.
Robinson, who primarily operates as a central midfielder, progressed through Southampton's youth academy and made his senior debut in September 2012.
"I'm really excited to get going," he said in an exclusive interview with bwfc.co.uk.
"Obviously it's going to be different after being at Southampton for so long, but I can't wait for a different challenge".